200 f Wisconsin Academy of Sciences, Arts, and Letters . 
Notes on Table A. 
All temperatures for American lakes have been computed by 
myself; the same is true for those European temperatures which 
are marked with a star. The data for Ammer See come from 
Geistbeck ’85 and Ule ’06; those for Tegern-See come from 
Breu, ’06. All other data are from Halbfass’ papers of ’05 and 
’ 10 . 
In the table annual gains of heat are shown by subtracting 
the winter temperature from that of the summer following, and 
are indicated thus in the table, ’95-’95. Losses of heat are 
shown by subtracting the winter temperature from that of the 
preceding summer, and are shown thus, ’95-’96. Both changes 
in temperature are taken as the basis for computing the annual 
heat budget. Thus observations in two successive summers and 
the intervening winter afford a basis for stating two budgets. 
This is the method followed by Halbfass in the papers to which 
reference has been made. The formula is Dm (Tm s -Tm w ), in 
which Dm represents the mean depth in centimeters; Tm s , sum¬ 
mer mean temperature; Tm w , winter mean temperature. 
The summer heat-income is computed by subtracting 4° from 
the summer mean temperature and multiplying the remainder 
by the mean depth expressed in centimeters. The formula is 
Dm (Tm s -4). 
The variations in the number of calories reported for a single 
lake m the table are caused by a variety of conditions. Chief 
among them is the variation' in the temperature of the water 
in the different years. Exceptional seasons cause exceptional 
budgets. This may be well illustrated by the temperature of 
Traun-See in 1895. The winter temperature that year was only 
2.66°, or nearly 1.5° below the other winter temperatures re¬ 
ported. The summer temperature was high, though not so far 
above the average as to be obviously exceptional, but the com¬ 
bination caused a budget of nearly 50,000 cal., undoubtedly very 
close to the possible maximum. Probably 6,000 cal.—9,000 cal. 
of this total are due to the exceptionally low winter tempera¬ 
ture, which is considerably below that reported for any other 
European lake of approximately equal depth. A second case 
may be that of Mjosen in the summer of 1901, but this will be 
discussed further on. 
Secondly, the temperature of the particular period in which 
